A Structured Set of Higher-Order Problems

Abstract

We present a set of problems that may support the development of calculi and theorem provers for classical higher-order logic. We propose to employ these test problems as quick and easy criteria preceding the formal soundness and completeness analysis of proof systems under development. Our set of problems is structured according to different technical issues and along different notions of semantics (including Henkin semantics) for higher-order logic. Many examples are either theorems or non-theorems depending on the choice of semantics. The examples can thus indicate the deductive strength of a proof system.